Evaluate Sums and Differences Using 0, 1/2, and 1

Evaluate Sums and Differences Using 0, 1/2, and 1

Knowing which fractions are close to 1/2 or 1

helps determine the reasonableness of sums and differences.

Multiple Choice

In order to be a fraction that is equal to 1, the...

• numerator and denominator must be 1

• numerator and denominator should be the same number

• numerator should be bigger than the denominator

• numerator and denominator should be different numbers

Multiple Choice

Select the fraction that equals to 1

• 
  ​ $\frac{1}{3}$  
  
  

•  $\frac{4}{3}$  

•  $\frac{7}{7}$  

•  $\frac{1}{2}$  

Arronasia estimates the sum of

 $\frac{2}{5}$  +  $\frac{4}{5}$  

She thinks the sum is greater than 1. Do you agree? Why?

Multiple Choice

Which is NOT an equivalent fraction to one half?

• 2/4

• 2/3

• 4/8

• 3/6

What if the denominators are different? How do you determine if the sum is greater than or less than 1/2?

Remember a fraction equals 1/2 when the numerator is 1/2 of the denominator.

 $\frac{1}{4}$  +  $\frac{1}{8}$  <  $\frac{1}{2}$  
reasonable or not reasonable

How do you know? 

The denominators are different! You can think about the denominators on fractions strips. As the denominator gets bigger, the pieces get what?

Another way to determine if

 $\frac{1}{4}$  +  $\frac{1}{8}$  <  $\frac{1}{2}$  

• Make a list of the multiples of 4 and 8

• Have the least common multiple

• 4: 4, 8, 12, 16

• 8: 8, 16

• 8 is the least common multiple

 $\frac{1}{4}$  +  $\frac{1}{8}$  <  $\frac{1}{2}$  

• since 8 was the least common multiple of 4 and 8

• Convert the denominator of  $\frac{1}{4}$  to 8

•  $\frac{1}{4}$  x  $\frac{2}{2}$  =  $\frac{2}{8}$  

•  $\frac{2}{8}$  +, $\frac{1}{8}$  =  $\frac{3}{8}$  

•  $\frac{3}{8}$ <  $\frac{4}{8}$  so it's less than  $\frac{1}{2}$  

Multiple Choice

 $\frac{9}{10}$  -  $\frac{1}{8}$  <  $\frac{1}{2}$  

• reasonable

• not reasonable

Multiple Choice

 $\frac{5}{12}$  +  $\frac{5}{12}$  

• > 1

• < 1

• = 1